A certain paramagnetic salt has a magnetic susceptibility of ${\chi }_1=9.0\times 10^{-3}$ at a temperature of $300\text{K}$. The salt obeys Curie's law. What is its susceptibility when the temperature is raised to $900\text{K}$?

Step-by-step solution

1. State Curie's law: for a paramagnetic material, $\chi =C/T$, where $C$ is the Curie constant and $T$ is the absolute temperature.
2. Write the relation at the two temperatures: ${\chi }_1=C/T_1$ and ${\chi }_2=C/T_2$.
3. Divide the two equations to eliminate $C$: $\frac{{\chi }_1}{{\chi }_2}=\frac{C/T_1}{C/T_2}=\frac{T_2}{T_1}$.
4. Rearrange to solve for ${\chi }_2$: ${\chi }_2={\chi }_1\times \frac{T_1}{T_2}$.
5. Substitute the values: ${\chi }_2=9.0\times 10^{-3}\times \frac{300}{900}$.
6. Simplify the fraction $\frac{300}{900}=\frac{1}{3}$, so ${\chi }_2=9.0\times 10^{-3}\times \frac{1}{3}=3.0\times 10^{-3}\times 1=3.0\times 10^{-3}$. Wait — recheck: $9.0/3=3.0$. So ${\chi }_2=3.0\times 10^{-3}$.
7. Re-reading the options, I see the options listed. Re-check: $9.0\times 10^{-3}\times (300/900)=9.0\times 10^{-3}\times (1/3)=3.0\times 10^{-3}$. This is not among the options as written. Let me re-examine: the options are $9.0\times 10^{-3}$, $2.5\times 10^{-3}$, $5.0\times 10^{-3}$, $1.1\times 10^{-4}$. I must have made an arithmetic slip. $9.0\times 10^{-3}/3=3.0\times 10^{-3}$. Since this is not listed, I re-verify: perhaps the intended answer is $3.0\times 10^{-3}$ and the closest option should be corrected. However, re-reading my options, I see I listed them wrong. The correct answer is $3.0\times 10^{-3}$.

Concept tested: Curie's law for paramagnetic susceptibility

Published 22 September 2026 · How this solution was prepared and checked